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Q.

A circular disc D₁ of mass M and radius R has two identical discs D₂ and D₃ of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre D₁, as shown in the figure, will be :

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a

$3 {MR}^{2}$

b

$\frac{2}{3} {MR}^{2}$

c

${MR}^{2}$

d

$\frac{4}{5} {MR}^{2}$

answer is A.

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Detailed Solution

1332088

From the figure,

$I = I_{1} + I_{2} + I_{3} = I_{1} + 2 I_{2}$

$I = \frac{{MR}^{2}}{2} + 2 (\frac{{MR}^{2}}{4} + {MR}^{2})$

$I = \frac{{MR}^{2}}{2} + \frac{{MR}^{2}}{2} + 2 {MR}^{2} = 3 {MR}^{2}$

Hence the correct answer is $3 {MR}^{2} .$

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A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis OO', passing through the centre D1, as shown in the figure, will be :